Finding maximum of sinc in 0..1

>> Could you be more specific about the "duality"? I may be missing some
>part
>> of information here.
>
>You can interpolate between FFT bins or you can interpolate between
samples.
>The mathematics are the same, only the domain changes.

Aaaha, got it, got a little confused.


>> As for linear-phase - if we assume there won't be any filtering (the
>> oversampling itself isn't filtering as it doesn't change the spectrum
>> content), then if we find the actual true peaks, then this should be
the
>> real maximum for any oversampling rate imho and no overshoots can
happen.
>
>If you don't filter then your inserted samples are all zero-valued. That
>interpolation will be the same as if you didn't upsample at all.

Ok, yes, but we assume a steep linear-phase filter close to nyquist, where
there won't be much anyways. But you are right, it could probably
overshoot indeed, maybe it's not worth exploring after all...


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> Has anyone attempted to do it analytically (hence hopefully efficiently)?

I don't think an analytic approach is going to be very successful. Even if you're facing just a single nonzero sample, trying to compute the extrema of sinc(t) leads to the equation tan(t)=t, which AFAIK can only be solved numerically.

> I started messing with it and the derivatives (for the classic f' == 0)
> are just way too ugly. Numeric approach could work, but the accuracy would
> be lower again and it could take way too much CPU power.

On the numerical front you could try doing something like a golden section search (https://en.wikipedia.org/wiki/Golden-section_search). I'm not sure if the extra accuracy you could get this way would be worth the CPU expense though.

-Ethan